It seems fairly obvious that the solution is to allow denser construction in the city cores, as well as allowing smaller residences to be built (such as dormitories at the lower end).
Average rent for a 1 bedroom apartment in Seattle, WA is $1869 a month [1]. A PugetPass costs about $80 a month. Living in Seattle without a car costs $1949 a month, or $23.4k a year.
Average rent for a 1 bedroom apartment in St. Louis, MO is $817 a month [2]. A decent used car that will last at least four years before needing maintenance costs a total of $4000, or an average of $83 a month. The national average for car insurance is $815 a year [3] (Missouri's is even lower), coming out to $68 a month. Now let's assume your used car gets a modest 25MPG, gas costs $3.00 a gallon, and your work is 15 miles away, plus you drive 20 miles on weekends. That's $82 a month in gas. Living with a car in St. Louis costs $1050 a month, or $12.6k a year.
Living with a car in a driveable city is $900/month and $10.8k/year cheaper than living in a non-driveable city. By this metric, non-driveable cities have housing that is 85% more expensive.
[1] https://www.rentcafe.com/average-rent-market-trends/us/wa/se...
[2] https://www.rentcafe.com/average-rent-market-trends/us/mo/sa...
[3] https://www.thesimpledollar.com/how-much-does-car-insurance-...
I lived in Montreal and paid C$675 / month for a 1 bedroom apartment 5 minutes from a metro station and another C$79 per month for monthly STM pass. Throw in a few trips outside the city with a rental car and we're still under C$10k.
https://www.theglobeandmail.com/news/national/how-does-montr...
There are also much cheaper driveable cities (e.g. Knoxville, TN) and much more expensive non-driveable cities (e.g. San Francisco, CA). Also, more realistically, you would probably be commuting to the city center if you were driving. Rent in the suburb of Florissant, MO is only $618 a month [1]. And the average gas price in St. Louis is only $2.28 a gallon [2], and insurance in Missouri costs an average of only $57 a month [3].
That brings the cost of housing down to $820 a month or $9.8k a year. I'm sure you could get a cheaper and more reliable car as well.
[1] https://www.rentcafe.com/average-rent-market-trends/us/mo/fl...
[2] https://www.gasbuddy.com/USA/MO
[3] https://www.thesimpledollar.com/how-much-does-car-insurance-...
Median household income in Seattle is roughly $80k.
Even after taxes, you'll have more money leftover after rent & transportation without a car in a city like Seattle than you will after rent & transportation in a car-oriented town like St Louis.
https://www.nerdwallet.com/cost-of-living-calculator/compare...